中文摘要：

孔隙介质核磁共振（NMR）弛豫信号的多指数反演在NMR岩芯分析与测井解释中起着关键作用．为了在不同信噪比条件下快速反演出高分辨率的弛豫时间谱，本文利用NMR正演模拟信号以及实验室NMR岩芯分析数据，研究横向弛豫时间布点数、原始回波采集个数、时间域数据压缩方式等对反演结果的影响．同时，在不同信噪比（SNR）下对不同的反演算法（SVD、BRD、SIRT）进行比较，考察反演算法对信噪比的敏感程度，并讨论了相应的校正方法．另外，还分析了信噪比对长、短弛豫组分的影响．研究表明在充分采集有用回波的情况下，减少回波个数，反演得到的弛豫时间谱趋向发散；增加布点数可以提高分辨率，但是需要更多的计算时间；时间域数据压缩可以加快反演计算速度；不同算法对信噪比的敏感程度不同，发展相应的校正方法可以提高反演质量。

英文摘要：

Multi-exponential inversion of NMR relaxation signal has been widely used in petroleum industry both in core analysis for petrophysical studies and in logging interpretation for oil exploration. In order to get relaxation time distributions with high resolution in the case of the low SNR, we use the NMR numerical simulation data and experimental data of core analysis to analyze the effects of the number of pre-assigned relaxation bins, the number of spin-echo acquired, and the compression in time domain of the spin-echo trains on the inversions. Meanwhile, in order to find out the influence of SNR for different inversions, the results under different SNR are compared, and the correction methods are improved accordingly. In addition, the influence of SNR to the components with short relaxation times or long relaxation times is discussed in the paper. The results of the study indicate that reducing echoes brings more divergent long T2 distributions, giving more bins can get higher resolution but take more time for calculation, and data compressing in time domain can increase the calculating speed but does not change the shape of algorithms have the influence is different sensitivity to the signal-to-noise ratio and a possible way to improve the inversion quality. T2 distribution significantlies, the different using some adjustable parameters to correct the influence is a possible way to improve the inversion quality.